1

Enhanced magnetization and improved insulating character in

Eu substituted BiFeO3

T. Durga Rao1, R. Ranjith2 and Saket Asthana1,a)

1 Advanced Functional Materials Laboratory, Department of Physics, Indian Institute of Technology Hyderabad, Andhra Pradesh–

502205, India

2 Department of Materials Science and Metallurgical Engineering, Indian Institute of Technology Hyderabad, Andhra Pradesh–502205, India

AIP | Journal of Applied Physics 115, 124110 (2014).

http://dx.doi.org/10.1063/1.4869775

This is author version post print archived in the official Institutional Repository of

IIT-H

www.iith.ac.in

Enhanced magnetization and improved insulating character in Eu substituted BiFeO3

T. Durga Rao1, R. Ranjith2, Saket Asthana1*

1Advanced Functional Materials Laboratory, Department of Physics,

Indian Institute of Technology Hyderabad, Andhra Pradesh – 502205, India

2Department of Materials Science and Metallurgical Engineering,

Indian Institute of Technology Hyderabad, Andhra Pradesh – 502205, India

*Author for Correspondence: asthanas@iith.ac.in

ABSTRACT

The polycrystalline Bi1-xEuxFeO3 (x = 0, 0.05 and 0.1) ceramics were synthesized by

conventional solid-state route. X-ray diffraction studies and Raman measurements revealed that

the compounds crystallized in rhombohedral structure with R3c space group. In addition, a nominal

percentage of orthorhombic phase was observed in 10 mole% Eu substituted BiFeO3. Appearance

of weak ferromagnetism and significant increase in Néel temperature TN in the substituted

2

compounds were discussed on the basis of structural distortions. Enhanced remnant magnetization

of 75 memu/g and large coercive field of 6.4 kÖe were observed in 10 mole% Eu substituted

BiFeO3. Equivalent circuit model was employed to estimate the grain and grain boundary

contributions towards the electrical parameters such as resistance, conductivity etc. Non-Debye

type of relaxation was confirmed from impedance and electric modulus studies. The obtained

frequency variation of ac conductivity at different temperature obeys Jonscher’s power law and is

consistent with the correlated barrier hopping (CBH) model. Temperature variations of ac

conductivity explained that electronic hopping, oxygen vacancies movement and/or creation of

defects contribute to conduction in all the compounds.

I. INTRODUCTION

Materials which have simultaneous existence of ferroic orders such as ferroelectric,

(anti)ferromagnetic and or ferroelastic are called multiferroics. These materials are potential

candidates for device applications such as memory devices, microelectronics and spintronics.1,2

Among all materials, BiFeO3 (BFO) is fascinating and well-studied for several decades. BFO has

high Curie temperature (TC = 1103 K) and high Néel temperature (TN = 643 K).3,4 In bulk form,

its crystal structure stabilizes in rhombohedral structure with R3c space group. Ferroelectricity

arises due to the distortion induced by stereochemically active 6s2 lone pair electrons of Bi3+, while

the indirect magnetic exchange interaction between Fe3+ ions through O2- causes G-type

antiferromagnetic ordering. This G-type antiferromagnetic ordering is superimposed with space

modulated spiral structure (SMSS) of incommensurate wavelength 62 nm. However, synthesis of

single phase BFO is a challenging task. Presence of oxygen vacancies, mixed valence states of Fe

ions, impurity phases such as Bi2Fe4O9, Bi25FeO40 enhance the electrical conductivity which is a

serious drawback for device applications.5 To minimize the impurity phases and to reduce the

leakage currents, various attempts have been made such as i) adopting several processing

techniques,6-8 (ii) substitution of elements at Bi/Fe – site,8, 9 (iii) fabricating composites.10 The

most effective technique to tune the multiferroic properties is to create internal chemical pressure

with the substitution of elements at A-site or B-site. Lanthanides7,8 and IIA alkaline earth metals6

are substituted at A-site where as transition metals elements are substituted at B- site.11 Substitution

of divalent ions at A- site increases the oxygen vacancies6 in order to maintain charge neutrality.

This enhances the leakage current which leads to deterioration of electrical properties of the

compounds. Partial substitution of lanthanides at Bi - site not only effectively minimizes the

impurity phases and reduces the leakage current, but also improves both magnetic and electric

properties of BFO. While extensive studies on structural, magnetic, dielectric and ferroelectric

3

properties of lanthanide substituted BFO have been done, there have been very few reports on

conductivity studies and electric transport mechanism on this compound.8, 12-15

Macroscopic electrical properties of polycrystalline ceramics are determined by

microstructure such as grain and grain boundary distributions in the compound. To investigate the

electrical properties of polycrystalline ceramics, impedance spectroscopy is the most versatile tool.

These studies, over a wide range of frequency and temperature, will assist to assess the insulating

character of the compound for potential application.

In this communication, Eu is used as a substitute for Bi in BFO and its structural, magnetic

and electrical transport properties of resultant compound are studied. Eu is used as a substitute

because; i) smaller ionic size of Eu creates internal chemical pressure which distorts FeO6

octahedra and changes Fe – O – Fe bond angle and Fe – O bond distances. These changes suppress

the SMSS which induces weak ferromagnetism 8,9 and ii) the bond enthalpy of Eu - O bond

(475±10 kJ/mol) is greater than that of Bi - O bond (337±12.6 kJ/mol).16-18 Stronger bond enthalpy

of R - O bond (R = Rare earth) compared to Bi – O bond presumably reduces oxygen vacancies19,20

and improves insulating character which is essential in terms of the potential applications. Further,

it is also observed from our UV-Vis-NIR spectrophotometry studies (not shown here) that band

gap increases with Eu substitution which also supports the improved insulating character in the

substituted compounds.

II. EXPERIMENTAL

BiFeO3 (BFO) and Bi1-xEuxFeO3 (BEFO) [x = 0.05 (BEFO5), 0.1 (BEFO10)] polycrystalline

compounds were synthesized by conventional solid-state reaction using the high purity Bi2O3

(99.999%, Sigma-Aldrich, USA), Fe2O3 (99.98%, Sigma-Aldrich, USA) and Eu2O3 (99.9%,

Sigma-Aldrich, China) as starting materials. These powders were weighed in stoichiometric

proportions and ground thoroughly for 2 hrs. Ground powders were calcined at 780 °C for 2 hrs

and then at 815 °C for 3 hrs. After calcination, the powders were mixed with PVA and pressed

uniaxially in to pellets with 8 mm diameter and 1.5 mm thickness. These pellets were finally

sintered at 830°C for 3 hrs. Phase analysis of the compounds was confirmed by using X-ray

diffractometer (Panalytical X’pert Pro) with Cu Kα radiation (λ = 1.5406 Å) with the step size of

0.0167° over the angular range 20°≤ 2θ ≤ 90°. Microstructure characterization and compositional

analysis (EDAX) were carried out using field emission scanning electron microscopy (FESEM,

Carl Zeiss, Supra 40). Raman scattering studies were performed on polished pellet using a laser

micro Raman spectrometer (Bruker, Senterra) with an excitation source of 785 nm. The magnetic

properties were measured using PPMS with VSM assembly (Quantum Design, USA). Differential

4

scanning calorimetry (DSC) was performed using a TA-Q200 calorimeter at a heating rate of 10

°C/min under N2 atmosphere. Dielectric property assessments were performed on the compounds

with silver electrode using Wayne Kerr 6500B impedance analyzer.

III. RESULTS AND DISCUSSIONS

Fig. 1(a) shows the XRD patterns of BFO and BEFO compounds. Trace amounts of impurity

phases such as Bi25FeO40 and Bi2Fe4O9 were observed along with the main phase.4 Rietveld

refinement21 revealed that, all compounds were crystallized in the rhombohedral crystal structure

with R3c space group. However, an evolution of nominal percentage of orthorhombic phase with

Pnma space group was evident in BEFO10 compound. As shown in Fig. 1(b), with the increase of

Eu substitution, two Bragg’s peaks (104) and (110) shifted towards higher angle side and partially

overlapped. The relative intensity of (104) peak gradually decreased compared to (110) peak

intensity. Meanwhile, the intensity of a peak (006) at 37.6° which originates from rhombohedral

structure became weaker with Eu content. Moreover, a weak (111) reflection near 25.4o (marked

by an arrow) in BEFO10 compound is commonly observed which corresponds to Pnma phase.6

FIG. 1. (a) XRD patterns of BFO and BEFO compounds. and represent impurity phases corresponding to

Bi25FeO40 and Bi2Fe4O9 respectively. Arrow shows weak (111) reflection near 25.4o in BEFO10 compound (b) XRD

patterns of BFO and BEFO compounds near 31-33 o.

This clearly indicates that Eu substitution results in evolution of orthorhombic phase within the

major rhomobohedral phase. Coexistence of such Pnma phase with R3c phase was also reported

in the literature22 and also supported from our Rietveld refinement. Evolution of orthorhombic

5

phase could be explained on the basis of internal chemical pressure using Goldschmidt tolerance

factor t, defined as ( ) / 2( )A O B Ot r r r r where <rA> is the average radius at A-site and rB and ro

are the radii of Fe3+ and O2- respectively. The tolerance factor decreased with the Eu content. The

decrement in t leads to Fe3+ - O and Bi3+ / R3+ - O bonds under compression and tension

respectively. Cooperative rotation of oxygen octahedra takes place in order to reduce the induced

lattice stress.23 Substitution of relatively smaller size of Eu ion increases the relative rotation angle

of oxygen octahedra along the polarization direction which is [111] axis. This induced lattice

distortion suppresses the rhombohedral phase with the evolution of preferable lower symmetric

phases. The internal chemical pressure induced structural distortion modifies the Fe-O-Fe bond

angles and the Fe-O bond distances which are responsible for tuning multiferroic properties of

BFO. The lattice parameters, volume of the unit cell, bond angle and bond distance of BFO and

BEFO compounds with the reference of R3c phase (major-phase) are given in Table I.

Table I. Variation of the lattice parameters, volume of the unit cell, bond angle and bond distance of BFO and BEFO

compounds.

Composition ahex ( Å ) chex ( Å ) V ( Å )3 Fe-O-Fe Fe-O1( Å ) Fe-O2( Å )

x = 0 5.5794 (6) 13.8709 (6) 373.95(6) 153.2(7) 2.215(16) 1.860(17)

x = 0.05 5.5734 (6) 13.8393 (6) 372.30(3) 154.4(6) 2.125(15) 1.935(13)

x = 0.10 5.5714 (5) 13.8239 (8) 371.62(1) 156.9(9) 2.061(18) 1.980(2)

Scanning electron micrographs of BFO and BEFO compounds are shown in Fig. 2. It can

be seen that BFO has an average grain size around 9 µm with a few distinct pores. The effect of

Eu substitution on the grain size was clearly evident from the micrographs.

FIG. 2. FESEM micrographs of (a) BFO, (b) BEFO5 and (c) BEFO10 compounds.

Table II. Density, average grain size and grain size distribution and activation energies of BFO, BEFO5 and BEFO10

compounds.

Compound % of

relative

density

Average

grain

size

(µm)

Grain size

distribution

(µm)

Activation energy E (eV) from

σdc data for M″ vs

ω data lnσac vs 1000/T data at

100 kHz

6

Grain Grain

boundary Region

I

Region

II

Region

III

BFO 88 9 1.5-9.5 0.76 1.00 0.69 0.18 0.59 1.38

BEFO5 91 2 0.5-4.0 0.74 0.88 0.74 0.21 0.54 1.42

BEFO10 93 1 0.5-3.5 0.88 0.95 0.75 0.16 0.67 1.63

Eu substitution decreased the grain size, reduced porosity and improved the density of the

compounds. Densities of the compounds were measured by Archimedes principle. Density,

average grain size and grain size distribution of BFO, BEFO5 and BEFO10 compounds are given

in Table II. Improved density in BEFO compounds leads to better grain connectivity with reduced

porosity which was confirmed from the microstructural analysis. Eu3+ ions suppress the grain

growth due to their lower diffusivity which in turn decreases the grain size24 From energy

dispersive x-ray spectrum (not shown here), all the compounds showed Bi:Fe ratio approximately

1:1.

Raman spectra of BFO and BEFO compounds are shown in Fig. 3(a). The natural

frequency of each Raman active mode was obtained by fitting the spectra and de-convoluted them

into individual modes. According to the group theory, BFO with rhombohedral R3c symmetry has

13 Raman modes which can be represented in irreducible notation as = 4A1+9E.25,26 The letter

A represents the symmetric transformation of a molecule under the rotation about the principle

axis of symmetry. The letter E represents a twofold degenerate vibration. The low frequency modes

at 139, 172 and 231 cm-1 were assigned as A1-1, A1-2 and A1-3 respectively. The remaining peaks

at 129, 261, 276, 303, 346, 369, 432, 480 and 524 cm-1 were assigned as E modes27,28 and all these

modes are given in Table III. It is reported that in BFO, A1 modes at 139, 172 and 231 cm-1 and E

modes with frequencies less than 400 cm-1 are attributed to Bi – O bonds whereas the E modes

with frequencies greater than 400 cm-1 are attributed to Fe – O bonds.29 Fig. 3(b) shows A1 and E

modes of BFO and BEFO compounds between 100 and 200 cm-1. In real crystals, life times of

phonons are reduced due to the scatterings from defects, disorder, strain etc. The decrease in life

times of phonons leads to increase in FWHM as FWHM is inversely proportional to life times.

Substitution of Eu at Bi – site leads to A- site disorder which in turn increases the peak broadening

(FWHM) and decreases the intensity of the peak.30,31 The two strongest A1 modes at 139 and 172

cm-1 show blue shift due to the substitution of less atomic mass element (Eu) at Bi site.32

From these findings, it can be concluded that the Eu3+ ion replaces Bi3+ ion at A-site of

host BFO lattice. The E modes of BFO at 261, 276, 346, 369 cm-1 respectively shifted to 262, 280,

7

338 and 375 cm-1 with the increase of Eu substitution which corresponds to evolution of

orthorhombic phase.22 Further, the gradual hardening of E modes at 276 and 303cm-1 due to

variation in internal chemical pressure may be attributed to the destabilization of Fe cations and

the octahedral tilts as reported by Yang et al33 in pressure induced studies. The changes in E modes

with Eu-content as discussed above indicate the evolution of orthorhombic phase which is also

supported from XRD analysis.

FIG. 3. (a) Raman spectra of BFO and BEFO compounds and (b) A1 and E modes of BFO and BEFO compounds

between 100 and 200 cm-1.

Table III. Raman modes (cm-1) of BFO and BEFO compounds.

Raman mode (cm-1) BFO BEFO5 BEFO10

E 129 122 109

A1-1 139 141 142

A1-2 172 173 174

A1-3 231 228 229

E 261 261 262

E 276 279 280

E 303 303 309

E 346 339 338

E 369 370 375

E 432 431 426

A1-4 480 475 476

E 524 530 528

Fig. 4(a) shows the magnetization hysteresis loops of BFO and BEFO compounds at 300K.

BFO exhibits G-type antiferromagnetic structure (i.e., each Fe3+ ion is surrounded by six nearest

neighbours with antiparallel spins). G-type antiferromagnetic structure is superimposed with a

spiral spin structure of incommensurate wave length of 62 nm34 which cancels the net

8

magnetization and inhibits the linear magnetoelectric effect in bulk BFO.35 Variation of remnant

magnetization Mr and coercive field Hc with Eu substitution are given in Table IV.

Non-saturation in magnetization was observed up to the applied field of 5 kÖe which

indicates that all the compounds retained the intrinsic antiferromagnetic nature. However, with the

increase in Eu content, the spin structure (SMSS) was suppressed due to variations in Fe-O bond

distances and bond angles,36 which leads to appearance of weak ferromagnetism.

TABLE IV. Remnant magnetization Mr and coercive field Hc of BFO and BEFO compounds.

Compound Mr (memu/g) Hc (kÖe)

BFO 0.626 0.235

BEFO5 21 2.4

BEFO10 75 6.4

Enhanced magnetization and coercive field in BEFO10 compound are not due to the

presence of Bi2Fe4O9 and Bi25FeO40 impurities phases which are paramagnetic at room

temperature. Further, it is worth to mention that remnant magnetization (Mr = 0.075 emu/g)

increased by two orders of magnitude in BEFO10 compared to BFO. This large change in Mr could

be due to the presence of minor orthorhombic phase which in turn leads to the more pronounced

suppression of SMSS in BEFO1023. Based on the above discussion, the appearance of weak

ferromagnetism in the studied compounds can be attributed to the suppression of SMSS.

FIG. 4. (a) Isothermal magnetization plots of BFO and BEFO compounds at 300K. Inset shows the enlarge view (b)

Differential scanning calorimeter plots of BFO and BEFO compounds.

Differential scanning calorimeter (DSC) plots of BFO and BEFO compounds are shown in

Fig. 4(b). All DSC curves showed a minimum which correspond to a second order

antiferromagnetic – paramagnetic transition. For BFO, Néel temperature (TN) is observed to be

9

373oC which is well matched with the reported values.5 An increase in Néel temperatures was

observed for BEFO5 (TN = 377oC) and BEFO10 (TN = 399oC) compounds. However, K. Deepti et

al37 noticed insignificant changes in TN whereas W. H. Sung et al38 reported decrease in TN in Eu-

substituted BFO. The variation of TN with Fe – O – Fe bond angle can be explained by the

following equation.8,39

TN = JZS(S+1) cosθ (1)

Where J is the exchange constant, S is the spin of Fe3+; Z is the average number of linkages per

Fe+3 ions and is Fe – O – Fe bond angle. As the Eu content increased, the bond angle also

increased from153.2o (x = 0) to 156.9o (x = 0.1). In the above equation, TN is proportional to the

cosine of bond angle which increases with bond angle. Further, due to stronger bond enthalpy of

Eu – O compared to Bi – O bond, number of oxygen vacancies might be suppressed which may

lead to increase in Z towards ideal value of 6. Based on the above discussion, increase in TN is

expected and is in consistent with our observations. This can also be expected due to high Néel

temperature of EuFeO3 compound.40

Frequency variation of real part of impedance (Z′) of BFO and BEFO at different

temperatures are shown in Fig. 5(a) – (c). Presence of dielectric relaxation behaviour was evident

from the dispersion behaviour of Z′ in the low frequency regions. Decrement in Z′ with frequency

was due to the increase of hopping of charge carrier which leads increased ac conductivity.

Negative temperature coefficient of resistance (NTCR) character could be accounted in terms of

decrement in Z′ with temperature. Increase in Z′ with Eu substitution indicated that the bulk

resistance was improved.8,41 This may be due to increase in the effective potential barrier heights

with the structural distortions.15 Further, from our UV-Vis-NIR spectrophotometry studies,

increase in band gap of BFO (2.05 eV) with Eu substitution (not given here) towards the band gap

of EuFeO3 (3.69 eV)41 supports the above conclusion.

The temperature variation of complex impedance can be understood using the following

equations43,44

( , ) ( )

( )1

o

y T dZ Z T

j

(2)

Real and imaginary parts of complex impedance can be expressed as

Real part: 2 2

( , ) ( )( , ) ( )

1o

y T dZ T Z T

(3)

and imaginary part: *

2 2

( ) ( , ) ( )( , ) ( )

1o

y T dZ T Z T

(4)

10

Where ω is the angular frequency, τ is the relaxation time and y(ω, τ) represents distribution of

relaxation times.

FIG. 5. Frequency variation of real part of impedance (Zʹ) for (a) BFO, (b) BEFO5 and (c) BEFO10 compounds.

Frequency variation of imaginary part of impedance (Z″) for (d) BFO, (e) BEFO5 and (f) BEFO10 compounds. Insets

in figures 5 (a) – (c) and 5 (d) – (f) show the frequency variation of Zʹ and Z″ from temperature 165 °C to 210 °C

respectively.

Fig. 5(d) – (f) shows frequency dependence of the imaginary part of impedance (Z″) of

BFO and BEFO compounds. Above 165 °C, Z″ data is characterized by i) appearance of a peak

with a maximum value (Z″max) at a certain frequency, ii) asymmetrical broadening, iii) shifting of

Z″max value to higher frequency with the increase in temperature and iv) decrement of magnitude

of Z″max with the temperature. Appearance of peak indicates the presence of electrical relaxation

in the compounds. Asymmetric broadening suggests that there is a distribution of relaxation times.

Shifting of Z″max value to higher frequency with temperature indicates that these relaxations are

temperature dependent.8 In Eu substituted BFO compounds, Z″ peak became weak which is due

to the presence of indistinguishable relaxation times corresponding to grain and grain boundaries.

Generally, polycrystalline dielectric materials have grains separated by interfacial

boundary layers (grain boundaries). The corresponding features can be seen with two semi-circular

arcs in the complex impedance plots. Each semi-circular arc can be modelled in terms of electrical

equivalent circuit consisting of a parallel combination of a resistor R and a capacitor (or constant

phase element CPE) C as shown in Fig. 6. The impedance of the resultant circuit45 can be expressed

as

11

1 ( ) 1 ( )g gb

g gb

n n

g g gb gb

R RZ

j R C j R C

(5)

Where Rg and Rgb are grain and grain boundary resistance, Cg and Cgb are grain and grain

boundary capacitances and ng and ngb are relaxation time distribution functions respectively. The

value of n is a measure of deviation from ideal Debye behaviour. For an ideal Debye relaxation, n

should be unity46 and in reality its value varies from zero to unity.

FIG. 6. Schematic picture of parallel combination of resistor and capacitor for grain and grain bondary.

The observed data was fitted with two equivalent R-C parallel circuits corresponding to

grain and grain boundary effects as shown in Fig. 7. Presence of a single semi-circle arc indicates

that electrical relaxations in the material arise basically from the bulk material. Appearance of

second semi-circular arc in the low frequency region is due to the grain boundary effects. The low

frequency semi-circular arc is corresponding to the grain boundary and high frequency semi-

circular arc is corresponding to the grain. Each semi-circular arc can be ascribed as a parallel

combination of resistance, R and capacitance (or constant phase element CPE) C. The assignment

of these two semi-circular arcs to the electrical response due to grain interior and grain boundary

is consistent with the ‘‘brick-layer model’’.47

If there exits multi-relaxations in the material, the semi-circular arcs are depressed i.e.

dielectric relaxation deviates from ideal Debye relaxation behaviour. As the temperature increases,

the circular arc depresses, and the intercept of arc with the Zʹ axis shifts towards the origin in the

Nyquist plots. Shifting of intercept towards origin indicates decrease in bulk resistance of the

compound. The values of Rgb (grain boundary resistance) and Rg (grain resistance) were estimated

by fitting the Nyquist plots from 150 oC to 225 oC for all the compounds. With the increase in

temperature from 150 oC to 225 oC, the values of Rgb and Rg decreased respectively from 8.4 MΩ

to 1 MΩ and 0.9 MΩ to 42 kΩ for BFO, 5 MΩ to 0.18 MΩ and 1 MΩ to 66 kΩ for BHFO5 and

10 MΩ to 0.31 MΩ and 3 MΩ to 83 kΩ for BHFO10 compounds. This indicates that the

compounds showed NTCR character which is consistent with the Zʹ data. Grain boundary

resistance dominated over grain resistance at all temperatures for all the compounds. The value of

grain resistance increased with the substitution of Eu at any temperature. This indicates the

improvement in the barrier properties for the flow of charge carriers with the Eu substitution.

12

FIG. 7. Nyquist plots of (a) BFO, (b) BEFO5 and (c) BEFO10 compounds at different temperatures.

DC conductivity of the compounds were calculated from the equation,

dc

t

AR

(6)

Where t is the thickness of the pellet, R is the resistance (of the grain or grain boundary) of the

compound and A is the area of the electrode. Both grain and grain boundary conductivities

increased with the increase in temperature and followed Arrhenius relation. The activation energies

were obtained from the linear fitting of plot drawn between lnσdc and 1000/T. The activation

energies of grain and grain boundaries of BFO and BEFO compounds were given in Table II.

Complex electric modulus ( )M formalism is a powerful technique to study the electrical

response of the material. The electric modulus ( M ) is expressed as

oM M iM i C Z

( )o o oi C Z iZ C Z i C Z (7)

Where ω is the frequency of applied electric field and Co is the capacitance in vacuum.

Frequency variation of real part of electric modulus (Mʹ) plots of BFO, BEFO5 and BEFO10

compounds at different temperatures are shown in Fig. 8(a) – (c). Mʹ plot is characterized by very

small value (close to zero) at the low frequency region and increases with the increase in frequency

at all temperatures, indicating negligible electrode polarization phenomenon in the test material.48

Mʹ showed the dispersion which increased with the increase in frequency and shifted towards the

higher frequency side. Frequency variation of imaginary part of electric modulus (M″) at different

temperatures for BFO and BEFO compounds are shown in Fig. 8(d) – (f). The value of electric

modulus (M″) was calculated using the formula

OM C Z (8)

Frequency variation of M″ curves are characterized by i) appearance of peak at unique frequency,

at a given temperature, ii) significant broadening in the peak which indicates the presence of

distribution of relaxation times and hence the relaxation is of non-Debye type and iii) shifting of

13

peak position towards high frequency region with the rise of temperature which indicates the

relaxation process is thermally activated.

FIG. 8. Frequency variation of real part of complex electric modulus (Mʹ) plots for (a) BFO,(b) BEFO5 and (c)

BEFO10 compounds. Frequency variation of imaginary part of complex electric modulus (M″) plots for (d) BFO,(e)

BEFO5 and (f) BEFO10 compounds. Modulus master curves (M″/ M″max vs f/ fmax) for (g) BFO, (h) BEFO5 and (i)

BEFO10 compounds.

The frequency region below the maximum value of M″ (M″max) indicates the range of

frequencies for the charge carriers to perform long range hopping from one site to another site

where as frequencies above M″max, charge carriers perform short range hopping and these particles

are confined to their potential wells. The frequency ( max ) corresponding to the M″max gives the

most probable relaxation time (τmax) for the charge carriers and follows the Arrhenius law

/

maxaE kT

oe (9)

Where ωo is the pre exponential factor and Ea is the activation energy. The activation energies of

BFO and BEFO compounds, calculated from the slope of the plot drawn between ln(ωmax) and

1000/T , are given in Table II.

Variation of normalized imaginary part of electric modulus (M″/M″max) with normalized

frequency (f/fmax) for BFO and BEFO compounds are shown in Fig. 8(g) – (i). For a given

compound, all curves at different temperature merge on a single master curve which indicates that

all the dynamic processes occurring at these temperatures will have the same activation energy.

Fig. 9 shows the frequency dependence of ac conductivity of BFO and BEFO compounds

at different temperatures. The response of the material to the applied electric field is described by

14

the ac conductivity. These studies will be useful to investigate the nature of transport process in

the compounds.

FIG. 9. Frequency variation of ac conductivity of (a) BFO, (b) BEFO5 and (c) BEFO10 compounds.

The ac electrical conductivity was calculated by using the relation,

.a c tano r (10)

The frequency dependence of ac conductivity obeys Jonscher’s power law49:

. (0) s

a c A

(0) ( ) (11)

Where σ (0) is the dc conductivity and s is an exponent.

The frequency dependence part ( ) is generally explained on the basis of two

mechanisms. In the case of quantum mechanical tunnelling (QMT) through the barrier separating

the two localized sites, the value of s should be independent of temperature and should slightly

decrease with frequency50 while in the case of correlated barrier hopping (CBH), s should decrease

with increase in temperature.51 It was observed that, for BFO and BEFO compounds, s values

decreased with increase in temperature. Therefore, the observed data was consistent with the CBH

model and the conduction process was thermally activated.

Fig. 10 shows the Arrhenius plots of ac conductivity at different frequencies for BFO and

BEFO compounds. The temperature dependence of ac conductivity can be represented by the

Arrhenius equation

. exp( / )a c o E kT (12)

Where o is the electric conductivity at infinite temperature, k is the Boltzmann constant and E is

the activation energy. The activation energies were calculated at frequencies 1 kHz, 10 kHz, 100

kHz, 500 kHz and 1 MHz for BFO and BEFO compounds. The obtained values at 100 kHz for all

compounds were given in Table II.

15

FIG. 10. Temperature dependence of ac conductivity of (a) BFO, (b) BEFO5 and (c) BEFO10 compounds.

In region I (below 393K), conductivity was frequency dependent, but temperature

independent. The ac conductivity increased with the increase of frequency due to the increase of

hopping of charge carriers. In this region, strong frequency dispersion was observed in all the three

compounds. Activation energies were found to be decrease with increase in frequency. Low

activation energies were observed and attributed to the electronic hopping conduction. In region II

(393K – 503K), conductivity not only depends on temperature, but also on frequency. Contribution

of short range of oxygen vacancies to the conductivity is expected in this region. In region III

(503K – 573K), conductivity was frequency independent and temperature dependent. Conductivity

was attributed to long range movement of oxygen vacancies or creation of defects.14 Increase in

activation energies were found with the increase in temperature.

IV. CONCLUSIONS

The polycrystalline Bi1-xEuxFeO3 (x = 0, 0.05 and 0.1) compounds were synthesized by

conventional solid-state route. Compounds were crystallized in rhombohedral structure with R3c

space group. Further, a nominal percentage of orthorhombic phase with Pnma space group was

observed in 10mole% Eu substituted BiFeO3. Magnetization measurements showed that weak

ferromagnetism and significant increase in Néel temperature in Eu substituted compounds were

mainly due to the crystal distortions. Insulating character of BiFeO3 compound improved with Eu

substitution which is evident from the impedance studies. The obtained ac conductivity data obeys

Jonscher's power law and is consistent with the correlated barrier hopping (CBH) model. The

observed activation energies conclude that electronic hopping, oxygen vacancies movement and

creation of defects are the contributors to the ac conductivity.

16

ACKNOWLEDGEMENTS

Authors are grateful to the Department of Science and Technology (DST), Government of

India for their financial support under Fast Track scheme (SR/FTP/PS–065/2011) to carry out this

work.

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